Assertions, conditionals, and defaults

A logical framework that emphasizes the impact of affirmative assertions is investigated with respect to providing an interpretation for conditionals and defaults. We consider theories consisting essentially of monadic subsumption statements. For every such theory there is an associated domain of information states ordered by a specialization relation. We show how to naturally interpret intuitionistic conditionals in this information domain. Moreover, we study several ways to cope with defaults. In particular, we adapt the approaches of Poole and Reiter to our framework.